what is typical coupling coefficient for a toroid

Fowler, “ Molecular anapole moments,” Phys. Kimura, “ Magnetoelectric control of frozen state in a toroidal glass,” Nat. Fu, “ Unusual phase transitions in ferroelectric nano disks and nanorods,” Nature 432(7018), 737 (2004). Chupis, “ Progress in studying ferro electromagnetic crystals,” Low Temperature Phys. Zel’Dovich, “ Electromagnetic interaction with parity violation,” Sov. Our experiments demonstrate Q factor and FoM of 183 and 76, respectively, making these metasurfaces a strong candidate for practical applications where high Q resonances are crucial. Such multifold toroidal mode leads to resonances with exceptionally high quality factors because of significant reduction in radiation losses. We attribute the observation of high-quality factor toroidal modes to the strong inter-unit cell near field coupling of the induced magnetic field lines. The anti-aligned circulating surface currents are observed along the circumference of metal split rings which resulted in a head to tail arrangement of the magnetic dipoles across the unit cells. At resonance, magnetic dipoles akin to toroidal topology are excited in these structures. In this work, we have experimentally demonstrated a strategy for achieving toroidal resonances with high Q factor and FoM in single resonator based planar metamaterials. However, demonstrating toroidal modes with high Q factors is a challenging task in a typical metamaterial system. Such metamaterial systems can be attractive for sensors, lasing spasers, nonlinear devices, narrow band filters, etc. Because of strong electromagnetic field confinements, associated radiative losses in toroidal modes can be tailored to extremely low values leading to simultaneous high quality ( Q) factor and high figure of merit ( FoM) resonances. Very recently, toroidal resonances were observed in metamaterial systems too. The phenomena of toroidal resonances can lead to extraordinary strong confinement of electromagnetic energy inside a physical system.

What is typical coupling coefficient for a toroid